Manny's Bakery recently spent a total of $600 on new equipment, and their average hourly operating costs are $5. Their average hourly receipts are $35. The bakery will soon make back the amount it invested in equipment. What would the total expenses and receipts both equal?Write a system of equations, graph them, and type the solution.

We are given taht a bakery has expenses that equal a fixed cost of $600 plus $5 for every hour of operating cost, this means that the expenses "E" are given by:

[tex]E=600+5h[/tex]

Where:

[tex]\begin{gathered} E=\text{ expenses} \\ h=\text{ operating hours} \end{gathered}[/tex]

We are also given that the receipts are $35 per hour, therefore, the receipts are given by:

[tex]R=35h[/tex]

We get the system of equations:

[tex]\begin{gathered} E=600+5h,(1) \\ R=35h,(2) \end{gathered}[/tex]

Now, we want to determine where both equations will have the same value. To do that we graph both equations and determine their point of minterception, as follows:

By graphing both equations we have obtained that the Expenses "E" and the Receipt "R" will intercept at the point

[tex](20,700)[/tex]

Where 20 represents the number of hours and 700 the total expenses and receipts.

Therefore, they both have the same value of $700.